The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Identify Direct Proportion and Solve Simple Problems

In this worksheet, students will use information relating to groups of items to find the cost of a single item, then apply this to find the value of a differently-sized new group or to identify the best value for money.

'Identify Direct Proportion and Solve Simple Problems' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Direct and Inverse Proportion

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

The easiest way to solve all problems involving direct proportion is to start by finding the value of a single unit.

 

Let's look at this process in action in some examples below before we tackle some related questions.

 

 

 

A gold ballpoint pen in a box   

 

e.g. If 8 pens cost £5.28, what is the cost for 5 pens?

 

Firstly, we need to find the cost of 1 pen.

 

We can lay out our findings in a table like this:

 

Pens Cost
8   £5.28
1 £5.28 ÷ 8 £0.66
5 £0.66 × 5 £3.30

 

 

 

A triangle of cheese with holes

 

e.g. 12 blocks of cheese make sandwiches for 48 people.

How many people can sandwiches be made for with 30 blocks of cheese?

 

Firstly, let's find out how many sandwiches can be made from 1 block of cheese:

1 block will make 48 ÷ 12 = 4 sandwiches

 

So 30 blocks of cheese will make sandwiches for:

30 × 4 = 120 people

 

 

 

Now you have a pen and a cheese sandwich, it's time to solve some problems using these skills!

 

In this activity, we will use information relating to groups of items to find the cost of a single item, then apply this to find the value of a differently-sized new group or to identify the best value for money. 

Box of 12 eggs

 

What is the cost of 60 eggs when 12 eggs can be bought for £2.10?

£10.25

£9.75

£10.60

£10.50

Collection of fizzy drinks in cans

 

If 8 cans of fizzy drinks cost £5.60, how much do 5 cans cost?

£3.50

£4.30

£3.75

£4.25

Silver can spilling pink paint out

 

If 12 litres of paint cost £45, how much do the following amounts cost?

 

Show all your answers to 2 decimal places.

£3.50

£4.30

£3.75

£4.25

Silver DVD player

If 8 of the same DVDs cost £96, how many DVD's can be bought for £60?

£3.50

£4.30

£3.75

£4.25

Black notebook

 

Mindy buys 12 pens for £7.80 and 6 notebooks for £10.50.

 

How much does Mindy pay altogether for 7 pens and 4 notebooks?

£3.50

£4.30

£3.75

£4.25

Loaf of cake with currants

 

Below is a recipe for a fruit cake that serves 6 people.

 

175 g dried fruit; 50 g candied peel; 120 ml of water; 175 g butter; 180 g caster sugar; 3 large eggs; 450 g flour

 

Calculate the alternative amount of ingredients required for the scenarios below.

 

£3.50

£4.30

£3.75

£4.25

Pile of $100 bills

 

Tracey changed £50 into dollars for her holiday to America.

The exchange rate was £1 = $1.55.

 

Use this information to answer the questions below. 

£3.50

£4.30

£3.75

£4.25

Yellow lorry shown from the side

 

A lorry uses 35 litres of fuel to travel 250 km.

 

Use this information to answer the questions below. 

£3.50

£4.30

£3.75

£4.25

Group of 6 apples

 

A farm shop sells apples at £9 for a 12.5 kg bag.

 

The same apples cost £1.83 for a 2.5 kg bag at the supermarket.

 

Where are the apples better value, at the farm shop or at the supermarket?

Farm shop

Supermarket

Cup of black coffee in a red cup

 

The Coffee Cabin sells coffee in three different sizes of cups:

£2.25 for 175 ml

£2.75 for 250 ml

£3.75 for 300 ml

 

Which size cup of coffee is the best value for money?

175 ml

250 ml

300 ml

  • Question 1

Box of 12 eggs

 

What is the cost of 60 eggs when 12 eggs can be bought for £2.10?

CORRECT ANSWER
£10.50
EDDIE SAYS
First, we need to find the cost of 1 egg: £2.10 ÷ 12 = £0.175 or 17.5 p Now we need to multiply this value by 60, to find the cost of the new amount of eggs: 0.175 × 60 = £10.50 You may have noticed that 12 × 5 = 60, so we could have found this answer using this alternative calculation too: £2.10 × 5 = £10.50
  • Question 2

Collection of fizzy drinks in cans

 

If 8 cans of fizzy drinks cost £5.60, how much do 5 cans cost?

CORRECT ANSWER
£3.50
EDDIE SAYS
Let's find the cost of one can to start: £5.60 ÷ 8 = £0.70 or 70 p Then multiply this by the new total (5): 0.70 × 5 = £3.50 It's as simple as that!
  • Question 3

Silver can spilling pink paint out

 

If 12 litres of paint cost £45, how much do the following amounts cost?

 

Show all your answers to 2 decimal places.

CORRECT ANSWER
EDDIE SAYS
As we are finding multiple amounts from our single unit price, it may be helpful to use a table here:
Litres of paint Cost per litre
12    £45
1 £45 ÷ 12 £3.75
3 £3.75 × 3 £11.25
5 £3.75 × 5 £18.75
8 £3.75 × 8 £30
22 £3.75 × 22 £82.50
  • Question 4

Silver DVD player

If 8 of the same DVDs cost £96, how many DVD's can be bought for £60?

CORRECT ANSWER
EDDIE SAYS
We just need to follow the same process as usual to start with, then change the final step at the end. £96 ÷ 8 = £12 per DVD This time we know the amount spent and we have to work backwards to find the number of DVDs. So instead of multiplying, we need to divide instead: £60 ÷ 12 = 5 DVDs
  • Question 5

Black notebook

 

Mindy buys 12 pens for £7.80 and 6 notebooks for £10.50.

 

How much does Mindy pay altogether for 7 pens and 4 notebooks?

CORRECT ANSWER
EDDIE SAYS
Let's start by finding our single unit prices: £7.80 ÷ 12 = £0.65 per pen £10.50 ÷ 6 = £1.75 per notebook Then let's multiply these amounts by our new totals: £0.65 × 7 = £4.55 £1.75 × 4 = £7.00 Then let's add these two amounts together: £4.55 + £7.00 = £11.55
  • Question 6

Loaf of cake with currants

 

Below is a recipe for a fruit cake that serves 6 people.

 

175 g dried fruit; 50 g candied peel; 120 ml of water; 175 g butter; 180 g caster sugar; 3 large eggs; 450 g flour

 

Calculate the alternative amount of ingredients required for the scenarios below.

 

CORRECT ANSWER
EDDIE SAYS
This question is phrased slightly differently, but the principle remains the same. So this time we need to find the amounts required to make cake for one person. Flour 450 g ÷ 6 = 75 g needed to make cake for one person 75 × 11 = 825 g Eggs 3 ÷ 6 = 0.5 eggs needed to make cake for one person 0.5 x 16 = 8 eggs Be careful not to get the division the wrong way round, which is easily done on questions such as this. Probably because we are thinking about cake...
  • Question 7

Pile of $100 bills

 

Tracey changed £50 into dollars for her holiday to America.

The exchange rate was £1 = $1.55.

 

Use this information to answer the questions below. 

CORRECT ANSWER
EDDIE SAYS
The skills we have been practising are really useful to have when we need to convert currency. We need to multiply when converting from pounds to a foreign currency; and do the opposite when we return home, so divide when converting a foreign currency back into pounds. £50 × 1.55 = $77.50 $30 ÷ 1.55 = £19.35
  • Question 8

Yellow lorry shown from the side

 

A lorry uses 35 litres of fuel to travel 250 km.

 

Use this information to answer the questions below. 

CORRECT ANSWER
EDDIE SAYS
We need to find the distance which can be travelled on 1 litre of fuel first: 250 ÷ 35 = 7.14 km per litre To find how far can be travelled on 50 litres, we need to multiply this amount by 50: 7.14 × 50 = 357 km To find how many litres would be needed to travel 400 km, we need to divide by this amount: 400 ÷ 7.14 = 56 litres (to the nearest litre)
  • Question 9

Group of 6 apples

 

A farm shop sells apples at £9 for a 12.5 kg bag.

 

The same apples cost £1.83 for a 2.5 kg bag at the supermarket.

 

Where are the apples better value, at the farm shop or at the supermarket?

CORRECT ANSWER
Farm shop
EDDIE SAYS
Let's find the cost for a single kg of apples in both shops, then compare them. Farm shop: £9.00 ÷ 12.5 = £0.72 Supermarket: £1.83 ÷ 2.5 = £0.732 So apples are more than a penny cheaper at the farm shop.
  • Question 10

Cup of black coffee in a red cup

 

The Coffee Cabin sells coffee in three different sizes of cups:

£2.25 for 175 ml

£2.75 for 250 ml

£3.75 for 300 ml

 

Which size cup of coffee is the best value for money?

CORRECT ANSWER
250 ml
EDDIE SAYS
Let's find the costs for a single ml of coffee in each cup size: £2.25 ÷ 175 = 0.0128 p per ml £2.75 ÷ 250 = 0.011 p per ml £3.75 ÷ 300 = 0.0125 p per ml The best value for money is the 250 ml cup, because this works out at the cheapest price per single ml. You can now use information relating to groups of items to find the cost of a single item, then apply this to find the value of a differently-sized new group or to identify the best value for money - now that's a useful skill to have!
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.